This work explores a new charge-dependent energy model consisting of van der Waals and polarization interactions between the quantum mechanical (QM) and molecular mechanical (MM) regions in a combined QM∕MM calculation. van der Waals interactions are commonly treated using empirical Lennard-Jones potentials, whose parameters are often chosen based on the QM atom type (e.g., based on hybridization or specific covalent bonding environment). This strategy for determination of QM∕MM nonbonding interactions becomes tedious to parametrize and lacks robust transferability. Problems occur in the study of chemical reactions where the “atom type” is a complex function of the reaction coordinate. This is particularly problematic for reactions, where atoms or localized functional groups undergo changes in charge state and hybridization. In the present work we propose a new model for nonelectrostatic nonbonded interactions in QM∕MM calculations that overcomes many of these problems. The model is based on a scaled overlap model for repulsive exchange and attractive dispersion interactions that is a function of atomic charge. The model is chemically significant since it properly correlates atomic size, softness, polarizability, and dispersion terms with minimal one-body parameters that are functions of the atomic charge. Tests of the model are examined for rare-gas interactions with neutral and charged atoms in order to demonstrate improved transferability. The present work provides a new framework for modeling QM∕MM interactions with improved accuracy and transferability.

1.
A.
Warshel
and
M.
Levitt
,
J. Mol. Biol.
103
,
227
(
1976
).
2.
M. J.
Field
,
P. A.
Bash
, and
M.
Karplus
,
J. Comput. Chem.
11
,
700
(
1990
).
3.
J.
Gao
,
Rev. Comput. Chem.
7
,
119
(
1995
).
4.
M.
Garcia-Viloca
,
J.
Gao
,
M.
Karplus
, and
D. G.
Truhlar
,
Science
303
,
186
(
2004
).
5.
B. A.
Gregersen
,
T. J.
Giese
,
Y.
Liu
,
E.
Mayaan
,
K.
Nam
,
K.
Range
, and
D. M.
York
,
Modelling Molecular Structure and Reactivity in Biological Systems
,
Proceedings of the WATOC 2005
, edited by
K. J.
Naidoo
,
J.
Brady
,
M. J.
Field
,
J.
Gao
, and
M.
Hann
, (
Royal Society of Chemistry
,
Cambridge
,
2006
), pp.
181
192
.
6.
B. A.
Gregersen
,
X.
Lopez
, and
D. M.
York
,
J. Am. Chem. Soc.
125
,
7178
(
2003
).
7.
B. A.
Gregersen
,
X.
Lopez
, and
D. M.
York
,
J. Am. Chem. Soc.
126
,
7504
(
2004
).
8.
J.
Gao
,
S.
Ma
,
D.
Major
,
K.
Nam
,
J.
Pu
, and
D.
Truhlar
,
Chem. Rev. (Washington, D.C.)
106
,
3188
(
2006
).
9.
T.-S.
Lee
,
C.
Silva-Lopez
,
M.
Matrick
,
W. G.
Scott
, and
D. M.
York
,
J. Chem. Theory Comput.
3
,
325
(
2007
).
10.
D.
Riccardi
,
P.
Schaefer
, and
Q.
Cui
,
J. Phys. Chem. B
109
,
17715
(
2005
).
11.
J. H.
Jensen
,
H.
Li
,
A. D.
Robertson
, and
P. A.
Molina
,
J. Phys. Chem. A
109
,
6634
(
2005
).
12.
D.
Major
,
D. M.
York
, and
J.
Gao
,
J. Am. Chem. Soc.
127
,
16374
(
2005
).
13.
T. D.
Poulsen
,
M.
Garcia-Viloca
,
J.
Gao
, and
D. G.
Truhlar
,
J. Phys. Chem. B
107
,
9567
(
2003
).
14.
I.
Tejero
,
M.
Garcia-Viloca
,
A.
González-Lafont
,
J.
Lluch
, and
D.
York
,
J. Phys. Chem. B
110
,
24708
(
2006
).
15.
W. L.
Jorgensen
and
J.
Tirado-Rives
,
J. Comput. Chem.
26
,
1689
(
2005
).
16.
Y.
Zhang
,
H.
Liu
, and
W.
Yang
,
J. Chem. Phys.
112
,
3483
(
2000
).
17.
Y.
Mo
and
J.
Gao
,
J. Phys. Chem. A
104
,
3012
(
2000
).
18.
M.
Štrajbl
,
G.
Hong
, and
A.
Warshel
,
J. Phys. Chem. B
106
,
13333
(
2002
).
19.
M.
Topf
and
W. G.
Richards
,
J. Am. Chem. Soc.
126
,
14631
(
2004
).
20.
M.
Klähn
,
S.
Braun-Sand
,
E.
Rosta
, and
A.
Warshel
,
J. Phys. Chem. B
109
,
15645
(
2005
).
21.
H.
Hu
,
Z.
Lu
, and
W.
Yang
,
J. Chem. Theory Comput.
3
,
390
(
2007
).
22.
W.
Thiel
,
Adv. Chem. Phys.
93
,
703
(
1996
).
23.
T.
Clark
,
J. Mol. Struct.: THEOCHEM
530
,
1
(
2000
).
24.
P.
Winget
,
C.
Selçuki
,
A.
Horn
,
B.
Martin
, and
T.
Clark
,
Theor. Chem. Acc.
110
,
254
(
2003
).
25.
W.
Thiel
, in
Handbook of Molecular Physics and Quantum Chemistry
, edited by
S.
Wilson
(
Wiley
,
Chicester
,
2003
), Vol.
2
, pp.
487
502
.
26.
M.
Kolb
and
W.
Thiel
,
J. Comput. Chem.
14
,
775
(
1993
).
27.
W.
Weber
and
W.
Thiel
,
Theor. Chem. Acc.
103
,
495
(
2000
).
28.
M. P.
Repasky
,
J.
Chandrasekhar
, and
W. L.
Jorgensen
,
J. Comput. Chem.
23
,
1601
(
2002
).
29.
I.
Tubert-Brohman
,
C. R. W.
Guimaraes
,
M. P.
Repasky
, and
W. L.
Jorgensen
,
J. Comput. Chem.
25
,
138
(
2003
).
30.
I.
Tubert-Brohman
,
C. R. W.
Guimarães
, and
W. L.
Jorgensen
,
J. Chem. Theory Comput.
1
,
817
(
2005
).
31.
M.
Elstner
,
T.
Frauenheim
,
E.
Kaxiras
,
G.
Seifert
, and
S.
Suhai
,
Phys. Status Solidi B
217
,
357
(
2000
).
32.
Q.
Cui
,
M.
Elstner
,
E.
Kaxiras
,
T.
Frauenheim
, and
M.
Karplus
,
J. Phys. Chem. B
105
,
569
(
2001
).
33.
D.
Riccardi
,
P.
Schaefer
,
Y.
Yang
 et al,
J. Phys. Chem. B
110
,
6458
(
2006
).
34.
K. W.
Sattelmeyer
,
I.
Tubert-Brohman
, and
W. L.
Jorgensen
,
IEEE Trans. Evol. Comput.
2
,
413
(
2006
).
35.
X.
Lopez
and
D. M.
York
,
Theor. Chem. Acc.
109
,
149
(
2003
).
36.
E. C.
Sherer
,
D. M.
York
, and
C. J.
Cramer
,
J. Comput. Chem.
24
,
57
(
2003
).
37.
T. J.
Giese
,
E. C.
Sherer
,
C. J.
Cramer
, and
D. M.
York
,
J. Chem. Theory Comput.
1
,
1275
(
2005
).
38.
K.
Nam
,
Q.
Cui
,
J.
Gao
, and
D. M.
York
,
J. Chem. Theory Comput.
3
,
486
(
2007
).
39.
P. L.
Cummins
and
J. E.
Gready
,
J. Comput. Chem.
19
,
977
(
1998
).
40.
M. S.
Formaneck
,
G.
Li
,
X.
Zhang
, and
Z.
Cui
,
J. Theor. Comput. Chem.
1
,
53
(
2002
).
41.
G.
Li
,
X.
Zhang
, and
Q.
Cui
,
J. Phys. Chem. B
107
,
8643
(
2003
).
42.
O.
Acevedo
and
W. L.
Jorgensen
,
J. Am. Chem. Soc.
127
,
8829
(
2005
).
43.
M. R.
Reddy
,
U. C.
Singh
, and
M. D.
Erion
,
J. Comput. Chem.
28
,
491
(
2007
).
44.
A.
Warshe
and
M.
Karplus
,
J. Am. Chem. Soc.
96
,
5677
(
1974
).
45.
J.
Gao
,
N.
Li
, and
M.
Freindorf
,
J. Am. Chem. Soc.
118
,
4912
(
1996
).
46.
T.
Vreven
and
K.
Morokuma
,
J. Chem. Phys.
113
,
2969
(
2000
).
47.
M.
Wanko
,
M.
Hoffmann
,
P.
Strodel
,
A.
Koslowski
,
W.
Thiel
,
F.
Neese
,
T.
Frauenheim
, and
M.
Elstner
,
J. Phys. Chem. B
109
,
3606
(
2005
).
48.
M.
Elstner
,
Theor. Chem. Acc.
116
,
316
(
2006
).
49.
C.
Alhambra
,
J.
Gao
,
J.
Corchado
,
J.
Villà
, and
D. G.
Truhlar
,
J. Am. Chem. Soc.
121
,
2253
(
1999
).
50.
M.
Garcia-Viloca
,
C.
Alhambra
,
D. G.
Truhlar
, and
J.
Gao
,
J. Comput. Chem.
24
,
177
(
2003
).
51.
H.
Lin
,
Y.
Zhao
,
O.
Tishchenko
, and
D. G.
Truhlar
,
J. Chem. Theory Comput.
2
,
1237
(
2006
).
52.
J.-Y.
Fang
and
S.
Hammes-Schiffer
,
J. Chem. Phys.
106
,
8442
(
1997
).
53.
J.-Y.
Fang
and
S.
Hammes-Schiffer
,
J. Chem. Phys.
107
,
8933
(
1997
).
54.
A.
Soudackov
and
S.
Hammes-Schiffer
,
J. Am. Chem. Soc.
121
,
10598
(
1999
).
55.
H.
Decornez
and
S.
Hammes-Schiffer
,
J. Phys. Chem. A
104
,
9370
(
2000
).
56.
S. P.
Webb
and
S.
Hammes-Schiffer
,
J. Chem. Phys.
113
,
5214
(
2000
).
58.
R.
Rjamani
,
K. J.
Naidoo
, and
J.
Gao
,
J. Comput. Chem.
24
,
1775
(
2003
).
59.
K.
Nam
,
J.
Gao
, and
D. M.
York
,
J. Chem. Theory Comput.
1
,
2
(
2005
).
60.
J.
Khandogin
,
B. A.
Gregersen
,
W.
Thiel
, and
D. M.
York
,
J. Phys. Chem. B
109
,
9799
(
2005
).
61.
B. A.
Gregersen
,
J.
Khandogin
,
W.
Thiel
, and
D. M.
York
,
J. Phys. Chem. B
109
,
9810
(
2005
).
62.
A. R.
Dinner
,
X.
Lopez
, and
M.
Karplus
,
Theor. Chem. Acc.
109
,
118
(
2003
).
63.
B. A.
Gregersen
and
D. M.
York
,
J. Comput. Chem.
27
,
103
(
2006
).
64.
B. A.
Gregersen
and
D. M.
York
,
J. Phys. Chem. B
109
,
536
(
2005
).
65.
P.
Schaefer
,
D.
Riccardi
, and
Q.
Cui
,
J. Chem. Phys.
123
,
014905
(
2005
).
66.
J.
Gao
,
P.
Amara
,
C.
Alhambra
, and
M. J.
Field
,
J. Phys. Chem. A
102
,
4714
(
1998
).
67.
Y.
Zhang
,
T.-S.
Lee
, and
W.
Yang
,
J. Chem. Phys.
110
,
46
(
1999
).
68.
I.
Antes
and
W.
Thiel
,
J. Phys. Chem. A
103
,
9290
(
1999
).
69.
N.
Reuter
,
A.
Dejaegere
,
B.
Maigret
, and
M.
Karplus
,
J. Phys. Chem. A
104
,
1720
(
2000
).
70.
D. M.
Philipp
and
R. A.
Friesner
,
J. Comput. Chem.
20
,
1468
(
1999
).
71.
M. S.
Gordon
,
M. A.
Freitag
,
P.
Bandyopadhyay
,
J. H.
Jensen
,
V.
Kairys
, and
W. J.
Stevens
,
J. Phys. Chem. A
105
,
293
(
2001
).
72.
J. Z. Z.
Ai
,
M.
Gao
,
D. W.
Zhang
, and
Y.
Zhang
,
Chem. Phys. Lett.
394
,
293
(
2004
).
73.
Y.
Mei
,
D.
Zhang
, and
J.
Zhang
,
J. Phys. Chem. A
109
,
2
(
2005
).
74.
Y.
Mei
,
C.
Ji
, and
J. Z. H.
Zhang
,
J. Chem. Phys.
125
,
094906
(
2006
).
75.
T. J.
Giese
and
D. M.
York
,
J. Chem. Phys.
120
,
9903
(
2004
).
76.
B. R.
Brooks
,
R. E.
Bruccoleri
,
B. D.
Olafson
,
D. J.
States
,
S.
Swaminathan
, and
M.
Karplus
,
J. Comput. Chem.
4
,
187
(
1983
).
77.
A. D.
MacKerell
, Jr.
,
J. Comput. Chem.
25
,
1584
(
2004
).
78.
D. M.
Perreault
and
E. V.
Anslyn
,
Angew. Chem., Int. Ed. Engl.
36
,
432
(
1997
).
79.
M.
Oivanen
,
S.
Kuusela
, and
H.
Lönnberg
,
Chem. Rev. (Washington, D.C.)
98
,
961
(
1998
).
80.
M.
Klähn
,
E.
Rosta
, and
A.
Warshel
,
J. Am. Chem. Soc.
128
,
15310
(
2006
).
81.
J.
Gao
and
X.
Xia
,
Science
258
,
631
(
1992
).
82.
F. J.
Luque
,
N.
Reuter
,
A.
Cartier
, and
M. F.
Ruiz-López
,
J. Phys. Chem. A
104
,
10923
(
2000
).
83.
D.
Riccardi
,
G.
Li
, and
Q.
Cui
,
J. Phys. Chem. B
108
,
6467
(
2004
).
84.
M.
Freindorf
,
Y.
Shao
,
T. R.
Furlani
, and
J.
Kong
,
J. Comput. Chem.
26
,
1270
(
2005
).
85.
W.
Thiel
and
A. A.
Voityuk
,
J. Phys. Chem.
100
,
616
(
1996
).
86.
T. J.
Giese
and
D. M.
York
,
J. Chem. Phys.
123
,
164108
(
2005
).
87.
D. M.
York
and
W.
Yang
,
J. Chem. Phys.
104
,
159
(
1996
).
88.
S.
Kita
,
K.
Noda
, and
H.
Inouye
,
J. Chem. Phys.
64
,
3446
(
1976
).
89.
R. J.
Wheatley
and
S. L.
Price
,
Mol. Phys.
69
,
507
(
1990
).
90.
J.
Piquemal
,
G.
Cisneros
,
P.
Reinhardt
,
N.
Gresh
, and
T. A.
Darden
,
J. Chem. Phys.
124
,
104101
(
2006
).
91.
T. J.
Giese
,
V. M.
Audette
, and
D. M.
York
,
J. Chem. Phys.
119
,
2618
(
2003
).
92.
K. T.
Tang
and
J. P.
Toennies
,
J. Chem. Phys.
80
,
3726
(
1984
).
93.
R.
Pellenq
and
D.
Nicholson
,
Mol. Phys.
95
,
549
(
1998
).
94.
R.
Pellenq
and
D.
Nicholson
,
Mol. Phys.
96
,
1001
(
1999
).
95.
A. J.
Thakker
,
J. Chem. Phys.
89
,
2092
(
1988
).
96.
K. T.
Tang
and
J. P.
Toennies
,
Surf. Sci. Lett.
279
,
L203
(
1992
).
97.
U.
Kleinekathöfer
,
K. T.
Tang
,
J. P.
Toennies
, and
C. L.
Yiu
,
J. Chem. Phys.
107
,
9502
(
1997
).
98.
S. F.
Boys
and
F.
Bernardi
,
Mol. Phys.
19
,
553
(
1970
).
99.
R. A.
Kendall
,
T. H.
Dunning
, Jr.
, and
R. J.
Harrison
,
J. Chem. Phys.
96
,
6796
(
1992
).
100.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
98
,
1358
(
1993
).
101.
Basis sets were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 6∕19∕03, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, U.S.A., and funded by the U.S. Department of Energy. The Pacific Northwest Laboratory is a multiprogram laboratory operated by Battelle Memorial Institue for the U.S. Department of Energy under Contract No. DE-AC06-76RLO 1830. Contact David Feller or Karen Schuchardt for further information.
102.
D. E.
Woon
and
T. H.
Dunning
, Jr.
,
J. Chem. Phys.
101
,
8877
(
1994
).
103.
See EPAPS Document No. E-JCPSA6-127-025735 for further discussion. This document can be reached through a direct link in the online article’s HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
104.
CRC Handbook of Chemistry and Physics
, edited by
D. R.
Lide
, 83rd ed. (
CRC
,
Boca Raton FL
,
2003
).

Supplementary Material

You do not currently have access to this content.